## ASSIGNMENT PROBLEMS

1. Write the state equation(s) for the following mechanical system of two gears. Assume that the cables always remain tight and all deflections are small.

2. Draw FBDs for the following mechanical system containing two gears.

3. Draw FBDs for the following mechanical system. Consider both friction cases.

4. Draw FBDs for the following mechanical system.

5. Develop a differential equation of motion for the system below assuming that the cable always remains tight.

6. Write the state equations for the following mechanical system. Assume that the cables always remain tight and all deflections are small.

7. Write the state equations for the following mechanical system. Assume that the cables always remain tight and all deflections are small.

8. Write the state equations for the following mechanical system. Assume that the cables always remain tight and all deflections are small.

9. A simplified model of a cam shaft driven lever is shown below.

a) Determine the equation of motion (differential equation) for the system as a function of theta.

b) Assume that L1 = 10.0cm and L2 = 4.0cm. Given an applied force of F=400N resulting in a deflection of y=-1.0cm, calculate the spring coefficient Ks.

c) Explicitly solve the differential equation to find theta as a function of time. The result should be left variable form.

d) Provide the system model as a state variable matrix.

e) Select a value for Jm that results in a natural frequency of 4Hz using the values provided in step b).